The present invention relates to the layup of
i. a multimaterial fully isotropic laminate that exhibits a concomitant stiffness isotropy in extension, shear, bending, and twisting; and PA1 ii a multimaterial quasi-homogeneous anisotropic laminate that has identical stiffness anisotropy in extension and bending as well as in shear and twisting PA1 "Sublaminate" refers to a part of a laminate, which consists of a group of plies (adjacent or detached) related to one another by the ply material, orientation, thickness, and so forth; PA1 "Midplane" refers to the plane containing all the midpoints in the thickness direction of the laminate; PA1 "Orientation angle" refers to the angle between the material axis (usually the fiber direction) of a ply and a reference axis fixed in the midplane of the laminate; PA1 "Extensional stiffness" relates the extensional force intensity on a laminate to the extensional strain on the laminate midplane; PA1 "Shear stiffness" relates the shear force intensity on a laminate to the shear strain on the laminate midplane; PA1 "Bending stiffness" relates the bending moment intensity on a laminate to the bending curvature on the laminate midplane; PA1 "Twisting stiffness" relates the twisting moment intensity on a laminate to the twisting curvature on the laminate midplane; PA1 "Weighting factor" is a conventional mathematical term and will be clarified in the Detailed Description; PA1 "Isotropy" refers to material properties that are the same in every direction (with infinite numbers of planes of symmetry); PA1 "Orthotropy" refers to material properties that vary with direction and have mutually perpendicular planes of material symmetry: PA1 "Anisotropy" refers to material properties that vary with direction and have no plane of material symmetry; PA1 "Nonisotropy" refers to orthotropy or anisotropy. (Applicants: In the field of composite technology, "anisotropy" and "directionality" are often used synonymously for nonisotropy. This convention is adopted in the present application.) PA1 i. a single-material fully isotropic laminate (hereinafter designated as FIL) that exhibits a concomitant stiffness isotropy in extension, shear, bending, and twisting; and PA1 ii. a single-material quasi-homogeneous anisotropic laminate (hereinafter designated as QHAL) that has identical stiffness anisotropy in extension and bending as well as in shear and twisting, PA1 i. a multimaterial fully isotropic laminate (hereinafter designated as MFIL) that exhibits a concomitant stiffness isotropy in extension, shear, bending, and twisting; and PA1 ii. a multimaterial quasi-homogeneous anisotropic laminate (hereinafter designated as MQHAL) that has identical stiffness anisotropy in extension and bending as well as in shear and twisting PA1 i. An MFIL provides the same stiffness reinforcement in all directions, which eliminates the concern for the "weak aspect" in the structural element and eases the engineering consideration of composite laminates. PA1 ii. An MQHAL, with identical anisotropy for both in-plane and out-of-plane stiffnesses, provides the maximum (and minimum) in-plane and out-of-plane reinforcements in the same direction. Thus, an MQHAL is a layup for weight reduction in a laminated structure. PA1 a multimaterial fully isotropic laminate that exhibits the concomitant stiffness isotropy in extension, shear, bending, and twisting; and PA1 ii. a multimaterial quasi-homogeneous anisotropic laminate that has identical stiffness anisotropy in extension and bending as well as in shear and twisting.
for the composite laminates requiring at least two different materials. In addition, layups of the multimaterial fully isotropic laminate relate to a substantially new category of the single-material fully isotropic laminate. The present invention improves over the prior art in the U.S. patent application Ser. No. 07/817,385 filed on Jan. 6, 1992, later U.S. Pat. No. 5,312,670 dated 17 May 1994, and offers further structural weight reduction and material cost saving.
A laminate is a flat plate or curved shell consisting of two or more plies stacked and bonded as an integral component for structural applications. Each ply is a uniform-thickness layer of material. FIG. 1 shows an exploded view of a typical flat laminate. The arrangement of the material, thickness, orientation, and stacking sequence of the plies is referred to as the "layup" of the laminate. The layup of a laminate is generally tailored to match the stiffness and strength requirements for loadings from various directions.
FIGS. 2(a) and 2(b) illustrate the definitions of the coordinate system and the mechanical loadings (extension, shear, bending, and twisting) on a flat laminate.
In this application,
For clarification and examples: each layer of a laminated safety glass is an isotropic material; most of the metallic alloys are considered isotropic materials; cloth is an orthotropic material; composite materials such as boron/epoxy and graphite are inherently anistropic or orthotropic materials. (Attachment 1)
The constituent material of a uniform-thickness ply may be homogeneous or heterogeneous (including porous material); isotropic or nonisotropic; honeycomb-like or otherwise mechanically formed; or of certain combination of the above. In the present application, however, the terms "material" and "material property" refer to the effective ply material and property that is computed by assuming the ply is homogeneous.
Therefore, the term "multimaterial" used for the present invention refers to the variation of the effective ply material property between plies, rather than the variation of the constituent material property within a ply.
To date, laminated plates and shells have found a wide range of applications in aerospace structures who, re high strength-to-weight and high stiffness-to-weight ratios are desired. Fiber-reinforced composite laminates such as graphite/epoxy and Kevlar/epoxy are used to combine with or to replace the conventional aluminum-, titanium-alloy structural components for weight reduction and other improvements.
FIGS. 3(a) and 3(b) show polar plots of the extensional and bending stiffnesses of an example, graphite/epoxy laminate, respectively. The length of d indicates the magnitude of the laminate stiffness with respect to the loading in direction .theta.. Since the laminate stiffnesses vary with .theta., the laminate is said to be anisotropic. Note that the degree of anisotropy in the extension and bending stiffnesses are different, which is typical of composite laminates.
The concept of in-plane isotropic laminates was discovered in 1953 by F. Weiren and C. B. Norris as described in "Mechanical Properties of a Laminate Designed to be Isotropic," Report No. 1841, Forrest Products Laboratory, Forest Service, U. S. Department of Agriculture, May 1953 (Attachment 2) FIGS. 4(a) and 4(b) show plots of the extensional and the bending stiffnesses of such laminates, respectively. In-plane isotropy is characterized by a circular pattern of extensional stiffness; while out-of-plane bending stiffness remains anisotropic. Hence, for the past few decades, a laminate with in-plane isotropy and a symmetric layup has been referred to as an "extensionally isotropic laminate" (hereinafter designated as EIL).
In a 1979 General Motors research report (EM-429, GM restricted), "Isotropic Composite Plates--A Conceptual Approach," K. M. Wu, one of the inventors of the present invention, described the approach for developing the laminate with stiffness isotropy in extension, shear, bending, and twisting. However, due to an incomplete solution scheme, no such laminate was discovered.
U.S. Pat. No. 5,312,670 (1994) awarded to K. M. Wu and B. L. Avery develops the layup of
which use plies of a single nonisotropic material throughout a laminate.
As illustrated in FIGS. 5(a) and 5(b), both extensional and bending stiffnesses of an FIL are indicated by circles for isotropy. This isotropy also exists in the shear and twisting stiffnesses of an FIL layup. The QHAL layup provides identical anisotropy in a laminate for both in-plane and out-of-plane stiffnesses. "Identical anisotropy" stipulates that the stiffness directionalities are identical with respect to extension and bending, as well as to shear and twisting. FIGS. 6(a) and 6(b) show polar plots of the extensional and bending stiffnesses of a QHAL, respectively. Although both stiffnesses are anisotropic, the anisotropy is identical with respect to the angle .theta..
Because Wu and Avery also published their invention of the single-material FIL and QHAL layup to the Journal of Composite Materials in October 1992, a few research institutes have since become interested in searching for multimaterial counterparts of FIL and QHAL. However, the first and only success has been achieved by the applicants as described in the present invention.
The present invention improves over the FIL and QHAL, and discovers the layup of
for composite laminates that require two or more materials. In addition to achieving the stiffness characteristics of FIL and QHAL illustrated in FIGS. 5(a), 5(b), 6(a), and 6(b), the MFIL and the MQHAL layups accommodate the multimaterial requirement and thus introduce further structural weight reduction and material cost saving. Moreover, the MFIL layup leads to the discovery of a substantially new category of FIL, as will be detailed later.
The MFIL and the MQHAL have distinctive applications for load-carrying laminates,
The approaches and models for generating these layups are closely related, as will be described in later sections.
Comparison with Other Inventions Related to Composite Materials
(1) U.S. Pat. No. 4,882,230 (1989) to S. B. Warner relates to a process for producing a multilayer polymeric film having dead bend characteristics which refers to the ability of the food-wrap film to remain folded after removal of the folding action (column 1, lines 28-31 of Warner's specification). Dead bend, as a term used by Warner, refers to an irreversible deformation that is not controlled by the bending stiffness of the material. In fact, Warner's process does not teach any method to affect the bending and twisting stiffness of the film. As a result, the bending and twisting stiffnesses of Warner's films are independent of each other and independent of the extensional and shear stiffnesses. In comparison, the present invention teaches the MFIL stacking sequence to concurrently achieve the isotropic extensional, shear, bending, and twisting stiffnesses of a laminate.
(2) U.S. Pat. No. 3,768,760 (1973) to L. C. Jensen teaches a multilayer-multidirectional composite laminate in which graphite fibers are designed to oppose in-plane shear stress (lines 5-8, claim 1 of Jensen). Jensen does not teach any method to affect the extensional, bending, and twisting stiffnesses. As a result, the extensional, shear, bending, and twisting stiffnesses of Jensen's laminates are entirely independent of one another. In comparison, the present invention teaches the MQHAL stacking sequence to reinforce the shear and twisting stiffnesses in the same direction and, concurrently, to reinforce the extensional and bending stiffnesses in the same direction of the laminate.
(3) U.S. Pat. No. 4,621,980 (1986) to Richard T. Reavely et al. relates a process for producing a tubular composite structure, wherein a plurality of fibrous materials are used for the damage tolerance and stiffness reinforcement of the structure. However, Reavely's process emphasizes the stiffness reinforcement only in one direction-the longitudinal axis of the tubular structure. As a result, the extensional, shear, bending, and twisting stiffnesses of its tube wall element are entirely independent of one another in every direction including the longitudinal axis for principal reinforcement. In comparison, the present invention teaches the MQHAL stacking sequence to relate the extensional and bending stiffnesses and to relate the shear and twisting stiffnesses in every direction of a composite panel. Consequently, an MQHAL layup reinforces the extensional and bending stiffnesses in the same direction and, concurrently, reinforces the shear and twisting stiffnesses in the same direction of a laminate.
(4) U.S. Pat. No. 4,848,745 (1989) to John R. Bohannan et al. relates a process for producing a laminated outer shell for a tubular object subject to splintering when impacted at high speed. Bohannan's process emphasizes stiffness reinforcement often in, but not limited to, the longitudinal axis of the tubular object. However, Bohannan's process does not teach any method to relate the extensional and bending stiffnesses or to relate the shear and twisting stiffnesses of the laminated shell in any direction. As a result, the extensional, shear, bending, and twisting stiffnesses of its shell element are entirely independent of one another in every direction. In comparison, the present invention teaches the MQHAL stacking sequence to relate the extensional and bending stiffnesses and to relate the shear and twisting stiffnesses in every direction of a composite panel. Consequently, an MQHAL layup reinforces the extensional and bending stiffnesses in the same direction and, concurrently, reinforces the shear and twisting stiffnesses in the same direction of a laminate.
(5) U.S. Pat. No. 4,946,721 (1990) to Christof Kindervater et al. teaches a process for producing an energy absorbing composites in the form of tubes or corrugated plates. Though mainly designed for energy absorption, the structure is typically stiffness-reinforced along the direction of pressure application. However, Kindervater's process does not teach any method to relate the extensional and bending stiffnesses or to relate the shear and twisting stiffnesses of the composite in any direction. As a result, the extensional, shear, bending, and twisting stiffnesses of its tube wall element (or corrugated plate element) are entirely independent of one another in every direction. In comparison, the present invention teaches the MQHAL stacking sequence to relate the extensional and bending stiffnesses and to relate the shear and twisting stiffnesses in every direction of a composite panel. Consequently, an MQHAL layup reinforces the extensional and bending stiffnesses in the same direction and, concurrently, reinforces the shear and twisting stiffnesses in the same direction of a laminate.
The stacking sequence to control the extensional, shear, bending, and twisting stiffnesses of a laminate is the central concept in the present invention. It would be unlikely for those skilled in the an to combine the teaching of the above inventions to achieve an MFIL or MQHAL, which are the subject matter of the present invention.